A construction of the rules for calculating with integers from the manipulation of algebraic expressions

This article presents part of a research developed in collaboration, by math education researchers and teachers of mathematics at the secondary level. The work addresses the problems encountered by teachers when teaching integers, and the difficulties students had grasping the concept, part...

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Autores principales: Detzel, Patricia, Ruiz, María Elena, Colipe, Lucas
Formato: Artículo revista
Lenguaje:Español
Publicado: Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación 2021
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Acceso en línea:https://revistas.unc.edu.ar/index.php/REM/article/view/32660
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spelling I10-R366-article-326602021-07-26T23:31:12Z A construction of the rules for calculating with integers from the manipulation of algebraic expressions Una construcción de las reglas de cálculo de los números enteros a partir de la manipulación de expresiones algebraicas Detzel, Patricia Ruiz, María Elena Colipe, Lucas Números enteros Actividad matemática Ruptura entre aritmética y álgebra Enseñanza escuela secundaria integers Mathematical activity gap between algebra and arithmetic Secondary school teaching This article presents part of a research developed in collaboration, by math education researchers and teachers of mathematics at the secondary level. The work addresses the problems encountered by teachers when teaching integers, and the difficulties students had grasping the concept, particularly in reference to the sign manipulation needed to carry on computations. Because of this premise, we all decided to study and make adaptations to an instructional proposal focused on the presentation of the negative integers together with that of algebra. We navigated a process of clarification that gave room for us to follow a meaningful path where the rules of addition, subtraction, and multiplication can be developed based on the knowledge of natural numbers. The role of algebra was fundamental in following this path. This article provides the analysis and reflections of the researchers and math teachers while adapting the original instructional approach. En este artículo presentamos parte de un trabajo desarrollado en un proyecto de investigación, en el que abordamos, en forma conjunta investigadores y profesores de matemática de escuelas secundarias, la problemática de la enseñanza de los números enteros desde una perspectiva colaborativa. Dicha problemática era una preocupación de los profesores de matemática, debido a las dificultades que observaban en sus alumnos, en particular en relación a la manipulación de los signos en los cálculos. Para ello acordamos en conjunto, estudiar y adaptar una propuesta de enseñanza en la que se aborda la introducción de los números negativos conjuntamente con el álgebra. Transitamos un proceso de esclarecimiento que nos permitió cargar de sentido un recorrido, en el que surgen las reglas de cálculo para la suma, resta y multiplicación de sumandos y sustraendos apoyadas en los conocimientos de los números naturales, donde las expresiones algebraicas tuvieron un rol fundamental. Desarrollamos en este artículo, parte de los análisis y reflexiones que llevamos a cabo profesores e investigadores en ese proceso para la adaptación de dicha propuesta. Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación 2021-04-05 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artículo evaluado por pares application/pdf https://revistas.unc.edu.ar/index.php/REM/article/view/32660 10.33044/revem.32660 Revista de Educación Matemática; Vol. 36 Núm. 1 (2021); 51-71 1852-2890 0326-8780 spa https://revistas.unc.edu.ar/index.php/REM/article/view/32660/33345 https://creativecommons.org/licenses/by-sa/4.0/
institution Universidad Nacional de Córdoba
institution_str I-10
repository_str R-366
container_title_str Revista de Educación Matemática
language Español
format Artículo revista
topic Números enteros
Actividad matemática
Ruptura entre aritmética y álgebra
Enseñanza escuela secundaria
integers
Mathematical activity
gap between algebra and arithmetic
Secondary school teaching
spellingShingle Números enteros
Actividad matemática
Ruptura entre aritmética y álgebra
Enseñanza escuela secundaria
integers
Mathematical activity
gap between algebra and arithmetic
Secondary school teaching
Detzel, Patricia
Ruiz, María Elena
Colipe, Lucas
A construction of the rules for calculating with integers from the manipulation of algebraic expressions
topic_facet Números enteros
Actividad matemática
Ruptura entre aritmética y álgebra
Enseñanza escuela secundaria
integers
Mathematical activity
gap between algebra and arithmetic
Secondary school teaching
author Detzel, Patricia
Ruiz, María Elena
Colipe, Lucas
author_facet Detzel, Patricia
Ruiz, María Elena
Colipe, Lucas
author_sort Detzel, Patricia
title A construction of the rules for calculating with integers from the manipulation of algebraic expressions
title_short A construction of the rules for calculating with integers from the manipulation of algebraic expressions
title_full A construction of the rules for calculating with integers from the manipulation of algebraic expressions
title_fullStr A construction of the rules for calculating with integers from the manipulation of algebraic expressions
title_full_unstemmed A construction of the rules for calculating with integers from the manipulation of algebraic expressions
title_sort construction of the rules for calculating with integers from the manipulation of algebraic expressions
description This article presents part of a research developed in collaboration, by math education researchers and teachers of mathematics at the secondary level. The work addresses the problems encountered by teachers when teaching integers, and the difficulties students had grasping the concept, particularly in reference to the sign manipulation needed to carry on computations. Because of this premise, we all decided to study and make adaptations to an instructional proposal focused on the presentation of the negative integers together with that of algebra. We navigated a process of clarification that gave room for us to follow a meaningful path where the rules of addition, subtraction, and multiplication can be developed based on the knowledge of natural numbers. The role of algebra was fundamental in following this path. This article provides the analysis and reflections of the researchers and math teachers while adapting the original instructional approach.
publisher Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación
publishDate 2021
url https://revistas.unc.edu.ar/index.php/REM/article/view/32660
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first_indexed 2024-09-03T22:36:49Z
last_indexed 2024-09-03T22:36:49Z
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